986 resultados para spin-Clifford bundles
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
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The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.
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In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.
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Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.
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The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.
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The conditions for the preparation of luminescent materials, consisting of Eu3+ ions entrapped in a titanium matrix, in the forma of a thin film, using the sol-gel process, are described. The films were obtained from sols prepared with TEOS and TEOT, in the presence of acetylacetone as the hidrolysis-retarding agent, using the dip-coating and spin-coating techniques. The influence of these techniques on the films based on titanium and silicon are presented. The Eu3+ was used as a luminescent probe. The films have been characterized by luminescence, reflection and transmittance. The thickness of the films could be related to the preparation procedure. Transparent thin films have been prepared by dip-coating technique.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Dyson's theory of conduction electron spin resonance (CESR) has been used in the limit d less than or equal to delta (d being the thickness of the sample and delta the skin depth of the microwave field) to obtain the microwave conductivity from the (A/B) ratio of the CESR absorbed power derivative. In this work we calculate the CESR absorbed power derivative using Kaplan's approach and show that the (A/B) ratio can be enhanced if asymmetrical penetration of microwave is used, which means that the microwave field enters into the sample from one of the faces. Therefore, the determination of the microwave conductivity from the (A/B) ratio of the CESR line can be performed for thinner samples. Experimentally, asymmetrical penetration can be obtained if one of the sample's faces is covered with a thin gold layer. The determination of microwave conductivity in conducting polymers films is among the possible applications of this method. (C) 2001 Elsevier B.V. Ltd. All rights reserved.